The Utility of Intersubjective Methods in Forecasting
SPUDM 2025
Jessica Helmer, Sophie Ma Zhu, Nikolay Petrov, Ezra Karger, Mark Himmelstein
Typical Testing vs. Forecasting
Unlike typical testing, where items have a known answer . . .
○ What’s the capital of Italy?
In forecasting, we do not know the answer at the time of testing
○ What will be the population of Lucca in 2050?
To measure forecasting ability, usually score with outcome (ground truth)
○ But that means we have to wait for items to resolve
Intersubjective Measures
Using peer comparisons to score forecasts instead of using outcomes
Why would this work?
Wisdom of the Crowds: when many predictions are aggregated, individual errors tend to cancel out
○ Making aggregated prediction typically accurate and reliable
(Atanasov & Himmelstein, 2023; Atanasov et al., 2017; Galton, 1907)
Intersubjective Measures
Using peer comparisons to score forecasts instead of outcomes
Why would this work?
Wisdom of the Crowds: when many predictions are aggregated, individual errors tend to cancel out
○ Making aggregated prediction typically accurate and reliable
These properties may make crowd aggregates a good substitution for the outcome to score in real time
(Atanasov & Himmelstein, 2023; Atanasov et al., 2017; Galton, 1907)
Simulation
N = 1,000 forecasters
○ Varying skill levels
K = 1,000 items
○ Specified item “noisiness”
Generated forecasts for each forecaster on each item
○ Skill defined how far off a forecaster’s forecast was expected to be
○ Forecasters were calibrated on the variance of the item
Simulation
Sampled combinations of:
○ N = [2, 4, 8, 16, 32, 64] forecasters and
○ K = [2, 4, 8, 16, 32, 64] items for
○ \(\sigma\) = [1, 2]
Scored each forecast with:
○ ground truth
○ intersubjective scoring (absolute distance from aggregate forecast of group of size N)
Which scoring measure captures forecasters’ skill better?
Simulation: \(\sigma = 1\)
Intersubjective scoring correlation increases with N
For N ≥ 16, intersubjective scoring captures original skill parameter better than ground-truth
Simulation: \(\sigma = 2\)
Increased variance affects ground-truth scoring but not intersubjective scoring
Intersubjective scoring has stronger correlations with skill at lower NK combinations than before
Intersubjective Measures
Types of intersubjective measures
Proxy Scoring
○ Scoring by a forecast’s distance from the aggregate forecast
Metapredictions
○ Explicit predictions about crowd aggregates
○ What would the average person predict that the population of Lucca will be in 2050?
Tested for their real-time scoring ability
Surprisingly successful at predicting forecasting accuracy
But have only been explored in the context of the Probability Elicitation Format (PEF)
(Himmelstein et al., 2023)
Present Study
- Are intersubjective measures still good predictors of forecasting accuracy in the (superior reliability) Quantile Elicitation Format (QEF)?
- Are proxy scores or metapredictions stronger predictors of forecasting accuracy?
Superforecasters
Previously identified skilled forecasters
Aggregating these superforecasters may serve as a better reference criterion than aggregating the general crowd
Proxy scoring with a superforecaster crowd aggregate has been an effective method
○ But has only been implemented between-subjects
(Karger et al., 2021; Tetlock & Gardner, 2015)
Present Study
Are intersubjective measures still good predictors of forecasting accuracy in the (superior reliability) Quantile Elicitation Format (QEF)?
Are proxy scores or metapredictions stronger predictors of forecasting accuracy?
- Are superforecaster aggregates a better reference criterion than general crowd aggregates?
Methods
Final wave of a longitudinal forecasting study (N = 894)
Forecasts on six items in the QEF
Metapredictions after each item:
○ What do you think the average person would predict?
○ What do you think a superforecaster would predict?
Additional sample of N = 42 superforecasters
(Himmelstein et al., 2025)
Scoring Methods
Scored each forecast with:
○ Ground Truth (own forecast distance from actual outcome)
○ proxy scoring (own forecast distance from crowd aggregate)
Proxy Crowd and Proxy Super
○ metaprediction accuracy (metaprediction distance from crowd aggregate)
Metaprediction Crowd and Metaprediction Super
Compared these scores to forecasting accuracy on separate set of thirty items
Aggregate Accuracy
Ground-truth score distributions
Superforecaster aggregate more accurate more often
Correlations
Superforecaster metapredictions and proxy scores strongest
Contributions to Forecasting Proficiency
How much variance in forecaster accuracy does each score explain?
Random effects for item and person, conducted dominance analysis
| Contribution | Proportion | |
|---|---|---|
| Proxy Super | .13 | .23 |
| Metaprediction Super | .12 | .22 |
| Proxy Crowd | .11 | .20 |
| Metaprediction Crowd | .10 | .18 |
| Ground Truth | .09 | .17 |
| \(R_{forecaster}^2\) | .54 | 1.00 |
(Azen & Budescu, 2003; Budescu, 1993; Luo & Azen, 2013)
Select Crowds
Proxy scores effective way of finding select crowds to aggregate
Discussion
Intersubjective measures still effective measure of forecasting ability
○ More reliable picture of the truth
Discussion
Intersubjective measures still effective measure of forecasting ability
○ More reliable picture of the truth
○ Less influenced by unpredictability in items
○ Superforecaster aggregates particularly useful
Can reduce measurement error by modifying the scoring criterion
○ Rather than modifying the task
References
Atanasov, P., & Himmelstein, M. (2023). Talent spotting in crowd prediction. In M. Seifert (Ed.), Judgment in Predictive Analytics. Springer.
Atanasov, P., Rescober, P., Stone, E., Swift, S. A., Servan-Schreiber, E., Tetlock, P., Ungar, L., & Mellers, B. (2017). Distilling the Wisdom of Crowds: Prediction Markets vs. Prediction Polls. Management Science, 63(3), 691–706. https://doi.org/10.1287/mnsc.2015.2374
Galton, F. (1907). Vox Populi. Nature, 75(1949), 450–451. https://doi.org/10.1038/075450a0
Himmelstein, M., Budescu, D. V., & Ho, E. H. (2023). The wisdom of many in few: Finding individuals who are as wise as the crowd. Journal of Experimental Psychology: General, 152(5), 1223–1244. https://doi.org/doi.org/10.1037/xge0001340
Himmelstein, M., Zhu, S. M., Petrov, N., Karger, E., Helmer, J., Livnat, S., Bennett, A., Hedley, P., & Tetlock, P. (2025). The Forecasting Proficiency Test: A General Use Assessment of Forecasting Ability. OSF. https://doi.org/10.31234/osf.io/a7kdx
Karger, E., Monrad, J., Mellers, B., & Tetlock, P. (2021). Reciprocal Scoring: A Method for Forecasting Unanswerable Questions. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.3954498
Tetlock, P. E., & Gardner, D. (2015). Superforecasting: The Art and Science of Prediction. Crown.
Wilkening, T., Martinie, M., & Howe, P. D. L. (2022). Hidden Experts in the Crowd: Using Meta-Predictions to Leverage Expertise in Single-Question Prediction Problems. Management Science, 68(1), 487–508. https://doi.org/10.1287/mnsc.2020.3919
Zhu, S. M., Budescu, D. V., Petrov, N., Karger, E., & Himmelstein, M. (2024). The psychometric properties of probability and quantile forecasts. Preprint.
Thank you!
Questions?
Contact: jhelmer3@gatech.edu
